The A340 was created because the airlines wanted an aircraft they could cross the atlantic ocean with (They couldn't with their twins because of ETOPS so far). So Airbus upgraded the A330 and added two engines. Because of the four engines, the plane was now allowed to cross the ocean.

However, four engines instead of two increase fuel cost dramatically (I assume). And the A340 is the same size as the A330. The A330 could fly with 2 engines. So why hasn't Airbus built the A340 with three engines instead of four. The fuel cost could have been reduced significantly without loosing the permission to cross the atlantic ocean. For example the MD-11 had three engines and also had permission to cross the ocean.

$\begingroup$@NoahKrasser: not aviation related, but a few years ago I changed my van with a 4.3 liter engine for a newer van with a 3.3 liter engine. To my surprise, fuel consumption was indistinguishable. I assume that if the engine doesn't use a significant amount of fuel to move itself, the absolute majority of the fuel burn is used for propulsion, and in conclusion the number of engines shouldn't make a big difference in fuel burn.$\endgroup$
– Martin ArgeramiJun 10 '17 at 22:56

$\begingroup$I think the premise of the question is entirely wrong... wasn't the A-330 always an ETOPS-approved aircraft? With the reason for the 4-engine A-340 being ability to carry more (fuel) weight in order to get longer range?$\endgroup$
– Ralph JJun 11 '17 at 19:49

$\begingroup$From what I have understood: Because engines weren't very reliable at the times of A330 and co., it was prohibited for twins to cross the ocean (They always had to be in range of a airport they can divert in case of an emergency).$\endgroup$
– Noah KrasserJun 12 '17 at 9:48

4 Answers
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Because the third engine would need to be near on centerline. That means in the tail.

Putting the engine in the tail significantly changes its design requirements.

Supporting an engine requires a lot of structural support. Then you need to run fuel to it. The effective height of the rudder is decreased. You probably need to switch over to a T-tail. The center of mass is also shifted which influences where the wings need to go.

In short, adding a single engine requires a redesign of the entire tail. While adding an engine to the wings is much simpler.

$\begingroup$Agreed for the most part, but why switch to t-tail? Neither DC-10/MD-11 nor L-1011 were t-tail. The h-stabs were mounted well beneath the #2 engine in both of those cases.$\endgroup$
– reirabJun 10 '17 at 15:38

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$\begingroup$@reirab that's why I said probably, it'll depend on how the main supporting structure is inside the tail and whether the new engine will get in the way$\endgroup$
– ratchet freakJun 10 '17 at 18:00

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$\begingroup$The placement of a tail mounted engine would produce a large change in the center of gravity. This would require a redesign to "move" the wings rearward, ie. add fuselage sections in front of the wing and/or remove sections from behind the wing. In addition going from 4 to 3 engines would require a total re-design of the fuel, electrical and hydraulic systems. All these changes mean that you have an entirely different aircraft which would have to be re-certificated from scratch. They would be better off with a blank sheet of paper.$\endgroup$
– Mike HJun 11 '17 at 4:24

Adding engines to the wings allows the minimum amount of changes to be made to the aircraft. Adding a third engine would require re-designing the tail section, and shifting the CG considerably at the same time. That would affect the airplane's handling characteristics so much that many calculations have to be redone.

In fact, the A330 and A340 are so similar that pilots are allowed to operate both of them with very little additional training. For example, Cathay Pacific pilots who are trained on the Airbus can operate both A330 and A340 in their fleet. This adds flexibility to an airline's schedule and reduce their training cost. If the A340 were a tri-jet, that would not be possible.

Project decisions like this based on are return on investment for the manufacturer. In other words, what will sales revenue be compared costs to engineer, certify, manufacture, and support be compared to sales revenue for the life of the project?

A center engine would require redesign of the empennage and all related systems. The certification requirements and cost to add an engine to the fuselage would be astronomically higher than hanging additional engines on the wing. Additional engine nacelles would have many parts and assemblies in common and would not impact as many other systems, flight controls, and aerodynamics to name a few.

Twin engine jets have had ETOPS ratings for decades, 757, 767, 737, etc. The engines on modern planes are gigantic, 8 ft dia fans and provide 50,000 to 60,000 lbs thrust, so they are plenty powerful.
Tri jet designs such as L1011 (beautiful design) and the DC10 had the issue of difficult maintenance of the high tail mounted engine and as technology improved, that configuration was phased out, although many tri's are still in service.